Problem

Source:

Tags: combinatorics, permutations, Romanian TST, 2017



Let n be a positive integer, and let Sn be the set of all permutations of 1,2,...,n. let k be a non-negative integer, let an,k be the number of even permutations σ in Sn such that ni=1|σ(i)i|=2k and bn,k be the number of odd permutations σ in Sn such that ni=1|σ(i)i|=2k. Evaluate an,kbn,k. * * *